Properties

 Label 114240.ji Number of curves 4 Conductor 114240 CM no Rank 0 Graph

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Show commands for: SageMath
sage: E = EllipticCurve("114240.ji1")

sage: E.isogeny_class()

Elliptic curves in class 114240.ji

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
114240.ji1 114240jq4 [0, 1, 0, -107905, -13678465] [2] 524288
114240.ji2 114240jq3 [0, 1, 0, -34305, 2262015] [2] 524288
114240.ji3 114240jq2 [0, 1, 0, -7105, -191425] [2, 2] 262144
114240.ji4 114240jq1 [0, 1, 0, 895, -17025] [2] 131072 $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 114240.ji have rank $$0$$.

Modular form 114240.2.a.ji

sage: E.q_eigenform(10)

$$q + q^{3} + q^{5} - q^{7} + q^{9} + 6q^{13} + q^{15} - q^{17} + 4q^{19} + O(q^{20})$$

Isogeny matrix

sage: E.isogeny_class().matrix()

The $$i,j$$ entry is the smallest degree of a cyclic isogeny between the $$i$$-th and $$j$$-th curve in the isogeny class, in the LMFDB numbering.

$$\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)$$

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels.